WORST_CASE(?,O(n^1)) * Step 1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: minus(f(x,y)) -> f(minus(y),minus(x)) minus(h(x)) -> h(minus(x)) minus(minus(x)) -> x - Signature: {minus/1} / {f/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h} + Applied Processor: NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(f) = {1,2}, uargs(h) = {1} Following symbols are considered usable: {minus} TcT has computed the following interpretation: p(f) = 6 + x1 + x2 p(h) = 5 + x1 p(minus) = 4 + 4*x1 Following rules are strictly oriented: minus(f(x,y)) = 28 + 4*x + 4*y > 14 + 4*x + 4*y = f(minus(y),minus(x)) minus(h(x)) = 24 + 4*x > 9 + 4*x = h(minus(x)) minus(minus(x)) = 20 + 16*x > x = x Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))